Sr Examen
Integral de 2*sqrtx*sqrt(1+(16*x^5)/9) dx
Solución
Ha introducido
[src]
1 / | | ___________ | / 5 | ___ / 16*x | 2*\/ x * / 1 + ----- dx | \/ 9 | / 0
$$\int\limits_{0}^{1} 2 \sqrt{x} \sqrt{\frac{16 x^{5}}{9} + 1}\, dx$$
Integral((2*sqrt(x))*sqrt(1 + (16*x^5)/9), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ _ /-1/2, 3/10 | 5 pi*I\ | 3/2 |_ | | 16*x *e | | ___________ 2*x *Gamma(3/10)* | | 13 | -----------| | / 5 2 1 | -- | 9 | | ___ / 16*x \ 10 | / | 2*\/ x * / 1 + ----- dx = C + -------------------------------------------------- | \/ 9 /13\ | 5*Gamma|--| / \10/
$$\int 2 \sqrt{x} \sqrt{\frac{16 x^{5}}{9} + 1}\, dx = C + \frac{2 x^{\frac{3}{2}} \Gamma\left(\frac{3}{10}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{10} \\ \frac{13}{10} \end{matrix}\middle| {\frac{16 x^{5} e^{i \pi}}{9}} \right)}}{5 \Gamma\left(\frac{13}{10}\right)}$$
Gráfica
Respuesta
[src]
_ /-1/2, 3/10 | pi*I\
|_ | | 16*e |
2*Gamma(3/10)* | | 13 | --------|
2 1 | -- | 9 |
\ 10 | /
------------------------------------------
/13\
5*Gamma|--|
\10/
$$\frac{2 \Gamma\left(\frac{3}{10}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{10} \\ \frac{13}{10} \end{matrix}\middle| {\frac{16 e^{i \pi}}{9}} \right)}}{5 \Gamma\left(\frac{13}{10}\right)}$$
=
=
_ /-1/2, 3/10 | pi*I\
|_ | | 16*e |
2*Gamma(3/10)* | | 13 | --------|
2 1 | -- | 9 |
\ 10 | /
------------------------------------------
/13\
5*Gamma|--|
\10/
$$\frac{2 \Gamma\left(\frac{3}{10}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{10} \\ \frac{13}{10} \end{matrix}\middle| {\frac{16 e^{i \pi}}{9}} \right)}}{5 \Gamma\left(\frac{13}{10}\right)}$$
2*gamma(3/10)*hyper((-1/2, 3/10), (13/10,), 16*exp_polar(pi*i)/9)/(5*gamma(13/10))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.